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Baker G.A., Gammel J.L. — The Padé Approximant in Theoretical Physics
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Название: The Padé Approximant in Theoretical Physics
Авторы: Baker G.A., Gammel J.L.
Аннотация: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.
As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression.
- Best operator approximation,
- Non-Lagrange interpolation,
- Generic Karhunen-Loeve transform
- Generalised low-rank matrix approximation
- Optimal data compression
- Optimal nonlinear filtering
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Рубрика: Математика /
Статус предметного указателя: Готов указатель с номерами страниц
ed2k: ed2k stats
Издание: 1
Год издания: 1970
Количество страниц: 378
Добавлена в каталог: 18.04.2010
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Предметный указатель
space of functions 172 225
Abramowitz 259 273 277 257
Accelerating convergence of a sequence 139
Akhiezer, N. I. 198 201 206 212 216 217
Alexander 95
Amati, D. 341 342 567
Analytic structure of scattering amplitudes 231 241 257 313 336
Analytic tanget matrix 311
Arndt, R. A. 350 367
Aspnes, D. 33 39
Atkinson, D. 242 249 250 252 256
Axilrod 50 95
Baker, G. A., Jr 1 2 6 7 8 12 16 19 20 29 31 32 33 35 36 38 42 45 46 47 61 70 71 72 73 93 95 101 106 128 137 169 177 182 185 186 189 193 195 198 199 200 217 227 229 233 238 239 242 247 259 287 308 331 334 367
Ball, J. S. 233 231 239
Banach space 188
Bander, M 242 256
Barker, J. A. 62 82 83 84 95
Beach, J. Y. 76
Bederson, B. 63 80 96
Bell, R. J. 52 85 94 95
Bernstein, R. B. 41 78 78 79 79 81 82 95
Berstein, F. 38
Bessis, D. 197 217 219 229 305 331 349 364 365 367
Bethe — Salpeter equation 197 220 257 289 334
Bethe, H. A. 56 95
Binning of Monte Carlo integrands 339
Bird, R. B. 90 91 93 96
Bootstraps 241—242 249 256
Borel continuation 87
Borel transform 184
Born expansion 312
Bounded analytic functions reduced to series of Stieltjes 18
Bounded operators 172
Bounds, on averages, using moment constraints 99
Bounds, on estimates of interatomic interaction 47 49
Bounds, on refractive index 70—71
Bounds, on relativistic terms in atomic interactions 84
Bounds, on sums of series, in cut plane 12
Bounds, on sums of series, of Stieltjes 18
Bounds, on sums of series, on real axis 11 46 256
Bounds, on sums of series, provided by generalized Pad approximants 25
Bounds, on thermodynamic quantities for Ising model 31
Bounds, on three-body dipole-dipole interaction 84
Breit, G. 333 367
Brooks, P. R. 81
Brown, L. 178 182
Buck, V. 79
Carleman’s criterion 11 202
Casimir — Polder formula 44 52
Casimir, H. B.G. 41 43 51 95
CDD poles 242
Chamberlain, G.E. 63 63 80 95
Chan, Y. 76
Chang, T. Y. 52 85 95
Chen, A. 197 217
Chew, G. F. 231 239 241 256
Chisholm, J. S. R. 8 35 36 38 174 176 178 179 180 182 307 331 334 335 367
Churchhill, R. V. 28 38
Cini 219 222 230
Cini — Fubini approximation 219 222
Clementi, E. 60
Coexistence curve 31
Common, A. K. 12 38 42 71 95 197 217 225 230 241 246 256
Compact operators 173
Complete continuity 173 209
Complete continuity, solution to integal equation with comletely continuous kernel 177
Construction of function which is difference of two series of Stieltjes from coefficients in power series expansion 36 137
Continued fractions 263
Continuous orthogonal expansions of Stieltjes transforms 131
Continuous orthogonal expansions of Stieltjes transforms, compared with Pad approximants 134 153 162
Continuous orthogonal expansions of Stieltjes transforms, convergence of 132
Continuous orthogonal expansions of Stieltjes transforms, generalizations 134
Contogouris, A. 250 256
Convergence examples 260 327 330
Convergence examples, conjectures 19
Convergence examples, generalized 21 193
Convergence examples, in mean 254
Convergence examples, in measure 227
Convergence examples, theorems 189 151
Convergence examples, theorems for continuous orthogonal expansions 130 132
Convergence examples, theorems for matrix elements of resolvent of symmetric operator 206 212
Convergence examples, theorems for Pad approximants 2 6—10 225 229 239 245
Cooper, J. W. 62 95
Copley, L. A. 197 218
Copson, E. 14 38
Coulomb scattering 285
Coupled channels 269 303 350
Critical exponents 32
Crowell, A. D. 90 91 95
Curtiss, C. F 90 91 93 96
Cutkosky, R.E. 343 367
Cziffra, P. 333 367
Dalgarno, A. 41 49 50 52 54 57 58 59 60 60 61 62 63 66 66 68 73 76 78 78 79 79 80 80 81 82 82 83 83 84 84 85 85 86 86 89 90 95
Davison, W. D. 41 49 50 62 63 76 78 79 80 81 84 85 89 95
de Montessus de Balloire, R. 10 38
Degges 73
Diagram representation of perturbation theory 146
Difference of two series of Stieltjes see Construction
Diffusion by random velocity field 139
Dipole dispersion force coefficients for alkali atoms 79
Dipole dispersion force coefficients for alkali atoms for alkali atom-diatomic molecules 83
Dipole dispersion force coefficients for alkali atoms for atomic helium 76
Dipole dispersion force coefficients for alkali atoms for atomic hydrogen 76
Dipole dispersion force coefficients for alkali atoms for diatomic gases 80
Dipole dispersion force coefficients for alkali atoms for inert gas-alkali atom 81
Dipole dispersion force coefficients for alkali atoms for inert gas-alkali atom, -diatomic molecule 82
Dipole dispersion force coefficients for alkali atoms for inert gases 78
Dipole oscillator strength 43
Dipole-dipole contribution to atomic interactions 47
Direct interaction approximations 157 169
Dispersion force coefficient 43 86;
Dispersion relations 232
Domain of convergence see convergence
Domb, C. 30 38
Durin, R. 78
Dynamic dipole polarizability 44
Dyson equation for bubble propagator 297
Eisenbud, O. 304 332
Eisenschitz — London formula 43
Eisenschitz, R. 41 42 95
Electron-hydrogen scattering 285
Elias, D,K. 197 218
Energy spectrum function of velocity field 139
Epsilon algorithm 4 139
Epstein, S. 54 85 86 94 95 96
Error bounds see bounds
Eve, J. 32 38
Faddeev equation 280
Faddeev, L.D. 280 287
Fano, U. 62 95
Feldman, D. 178 182
Feynman graph calculations 304 335 342
Fisher, M. E. 29 30 32 38
Fivel, D. I. 178 182
Fourier transform 183
Franklin, P. 26 38
Fredholm method 171 231 246 256
Free energy 31 115
Friedman, A. 188 195
Fubini, S. 219 222 230
Fubini’s Theorem 187—188
Fugacity 29—30
Functional analysis 171
Futrelle, R.P. 95 100 128
Gammel — Baker approximants see Generalized Pad approximants
Gammel, J. L. 19 35 38 197 218 239 239 304 331
Gargantini, J. 12 38
Gegenbauer polynomials 276
Generalized functions 184
Generalized functions of noncompact support 194
Generalized Pad approximants 20 106 186 189
Generalized Pad approximants, connection with method of moments 216
Generalized Pad approximants, convergence of 21 193
Generalized Pad approximants, in N/D method 248
Gilbert, H. E. 32 38
Gill, P. 69 70 74 74 95
Glennon 66 66 97
Goldberger, M. L. 342 346 367
Gordon, R. G. 15 38 94 95 96 100 101 103 115 117 120 124 128
Goscinski, O. 94 96
Gotze, W. 33 39
Graben, H. W. 51 95
Graffi, S. 349 364 365 367
Grashin, A. F. 349 567
Grecchi, V. 349 364 365 367
Green’s function 140
Grisaru 342 346 367
Gronwall, T. H. 19 38
Guttinger, W. 183 184 186 193
Hadamard, J. 12 38
Hale, G. 318 331
Halmos, P. R. 227 230
Hamblen, D. 33 39
Hamburger moment problem see Moment problem
Hamburger, H. 15 38
Hamilton, J. 299 302
Haracz, R. D. 342 367
Hardy, G.H. 18 38 114 128
Harmonic solid see Simple harmonic solid
Harriman, J. 56 95
Haymaker, R. 258 272 273 279 287
Heat capacity of simple harmonic solid 115 121
Hecht, R 33 39
Heddle, D. W.O. 69 70 74 74 95 96
Heisenberg model 220
Helbing, R. 78
Helicity 291
Henrici, P. 12 38 39
Herglotz, G. 18 38
Hildebrand, F. B. 326 331
Hirschfelder, J. O. 41 51 76 90 91 93 96
Hoheisel, G. 171 172 173 177 182
Huckaby, D. 121 128
Hull, M. H., Jr 333 367
Hurst, R. P. 59 96
Inequalities obeyed by Pad approximants to series of Stieltjes 11
Integral equations 171
Internal energy of simple harmonic solid 115
Irreducible diagram expansion 129 156
Irreducible diagram expansion, condition for validity of certain manipulations on 169
Isenberg, C. 115 116 117 121 725
J-fraction 199 201
Jansen, L. 51 96
Jeffreys, B.S. 26 38
Jeffreys, H. 26 38
Jennings, R. E. 70 74 74 96
Jensen’s inequality for convex functions 114
Jensen’s inequality for convex functions, scattering 303
Johnson, R. E. 85 86 95
Jones, C. E. 254 256
Kadanoff, L. P. 33 39
Kane, J. 33 39
Karlin, S. 100 111 128
Karplus 41 42 45 48 52 54 59 62 63 65 67 68 70 71 72 75 76 83 85 87 88 89 94 95 96 101
Kato 217 218
Kernels defined 172
Kernels defined, exact solution of integral equation with kernel of finite rank 176
Kernels defined, rank 174
Khanna, B. N. 69 70 74 96
Kihara 51 96
Kim, J. K. 331
Kingston, A. E. 52 54 61 62 74 80 82 83 84 85 95
Kirkwood, J.G. 75 90 96
Kirn, M 69 70 96
Koch, J. 70 96
Kohn variational principle 221 223
Kohn variational principle, convergence of 226 275
Kolker, H. J. 54 67 68 71 72 76 96
Kowalski, K. L. 178 182 289 302
Kraichnan, R. H. 134 144 157 169 169
Kramer, H. L. 93 96
Kramers — Heisenberg dispersion formula 42 44
Kramers — Heisenberg dispersion formula, operators 173 225 246 250
Kramers — Heisenberg dispersion formula, potential scattering kernel with Yukawa potentials is 181
Krein, M.G. 100 111 128
Kubis, J. J. 304 331
Kyle, H. L. 286 287
Landorff, R. W. 78
Langhoff, P. W. 41 42 45 48 54 59 62 63 63 65 70 75 83 85 87 88 89 94 96 101
Lassila, K. E. 333 567
Le Roy function 28
Leader, E. 341 342 567
Lee, B. W. 178 752
Lee, T. D. 29 30 31 59
Leighton, R. 116 117 725
Leonard, P. J. 62 82 83 84 95
Lepore, J. V. 334 567
Levine, M. J. 220 250 289 302
Levinger, J. S. 74
Lewis, E. A. S. 33 39
Liggett, G. 74
Linear integral equations 171
Lippman — Schwinger equation 178—179 197 220 221
Littlewood, J. E. 114 725
London formula 75
London, F. 41 42 75 88 91 95 96
Lowdin, P. O. 76
Lyth, D. H. 250 253 256
MacDowell, S. W. 342 346 367
MacGregor, M. H. 333 341 350 367
Machida, S. 334 367
Mandelstam, S. 231 259 241 256 344 567
Margenau, H. 75 88 96
Markov, A. 100 725
Martin, A. W. 241 242 256
Mason, E. A. 75 90 91 96
Mass operator of quantum field theory 147
Masson, D. 150 170 197 275 231 240
Mattioli, G. 335 567
Mavroyannis, C. 88 90 96
McDonald, F.A. 35 55 197 275 239 259
McDonald, J.R. 5 59
Mclnnis, B. C. 279 257
McQuarrie, D. A. 100 725
Meath, W. J. 41 51 85 56 96
Melton, L. A. 100 707 725
Method of moments for operators in Hilbert space 197 206
Method of moments for operators in Hilbert space, as generalized Pad approximant for operators 216
Method of moments for operators in Hilbert space, convergence for matrix elements of resolvent of symmetric operator 212
Method of moments for operators in Hilbert space, special perturbation technique 217
Metropolis, N. 341 567
Meyer L. 51 96
Mignaco, J. A. 305 552
Mikhlin, S. G. 171 752
Milne — Thompson, L. 16 59
Moiseiwitsch, B. L. 221 230
Moment problem 15 100 185—186 194 198—199
Moment problem, Carleman’s criterion for determinateness of 202
Moment problem, indeterminate case 216
Moment problem, Stieltjes inversion formula 199
Moments 100 101 108 185 264
Moments of oscillator strength distributions 45 53
Moments of oscillator strength distributions, determined from optical dispersion and absorption data for heavier atoms and molecules 60
Moments of oscillator strength distributions, for atomic helium 57 63
Moments of oscillator strength distributions, for atomic hydrogen 55
Monchick, L. 90 91 96
Monte Carlo integration 337
Moore, C. E. 66 66 96
Moravcsik, M. J. 333 341 350 567
Morrison, I. H. 75 79 80 85 55 86 56 90 95
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